Once an enemy is lowered to 0 HP, are they dead or just knocked out? Do you have to reduce them to their negative Con score or is that mechanic strictly reserved for players?
When a creature’s hit points drop below 0, it becomes unconscious. When a creature’s hit points reach a negative total equal to its Constitution score, it dies. -- Core, page 12 under 'Hit points'
'Creature' would imply that the rules effect everyone.
Although there are some exceptions, such as Undead and Constructs
Not at risk of death from massive damage, but is immediately destroyed when reduced to 0 hit points -- Bestiary page 307 and 310 under Constructs and Undead traits
But from a GMing standpoint it won't make much difference to house-rule 'minions die at HP:0', unless your group likes to take prisoners.
All characters and enemies follow the same conditons rules.
The character's hit points are reduced to a negative amount equal to his Constitution score, his Constitution drops to 0, or he is killed outright by a spell or effect. The character's soul leaves his body. Dead characters cannot benefit from normal or magical healing, but they can be restored to life via magic. A dead body decays normally unless magically preserved, but magic that restores a dead character to life also restores the body either to full health or to its condition at the time of death (depending on the spell or device). Either way, resurrected characters need not worry about rigor mortis, decomposition, and other conditions that affect dead bodies.
But GM can considers monsters dead below 0 HP to be "dead". It's only really matter when you don't want to kill your enemy (ex: humain opponent)
Depends on the enemy. Undead "die" when they reach to 0 HP, summoned creatures vanish when they reach to 0 HP, etc. But most natural creatures (like humanoids) just fall unconscious when their HP goes below 0.
If the HP reaches exactly 0, then they are disabled. If a creature performs a standard action it takes one more point of damage. You can read more about this condition here.
Reducing a creature or a PC to zero CON score kills them immediately, it's not only reserved for players.
I tend to say "yes" when I run games. This is simply because some enemies, like Orcs, have traits or feats, like ferocity or Diehard, where they can continue fighting below 0 hp, though in a staggered state. If enemies just die at 0 hp, then the balance of your encounters gets thrown off a bit.